Capacitors & Dielectrics 02 |

OPENING QUESTIONS: A) What is the *simplist* definition for capacitance? B) Let's say we have a cylinder of length ℓ made of some sort of conducting material that is surrounded (" 1)Let's get someone up here to set this up 2) And someone else to continue 3) And someone to finish
ANSWER:
C) If we know the total charge
ANSWER:
OBJECTIVE: I will be able to calculate the capacitance between two charged plate capacitors, cylindrical conducts and spherical conductors after today's class. WORDS/FORMULAE FOR TODAY TERMS:
CONSTANTS:
UNITS: - Capacitance = C
- (SI Units "farads" = f)
- C = Q/∆V
- farads are always positive
- capacitance measures ability of the system to store charge
- 1 farad is a MASSIVE amount of storage so we will typically talk in microfarads (μF = 10
^{-6}F) or picofarads (pF = 10^{-12 F})
FORMULAE: - Capacitance:
- C = ε
_{o}A/d (for a parallel plate capacitor) - C = Q/∆V (generally)
- C = ε
- Electrical Field: For a parallel plate capacitor: E= σ/ε
_{o}
WORK O' THE DAY: My annotated solution for capacitance of a spherical capicitor is below:
════════════════════ Let's revisit a simple parallel plate capacitor: 1) Why is this 'device' called a capacitor? 2) How is it that the negatively charged plate becomes negatively charged? (think freely roaming electrons) 3) How is it that the positively charged plate becomes positively charged? (think freely roaming electrons) 4) If capacitance is a measure of how much electrical energy a capacitor can store, does that mean that farads are = to jules? Why or why not? Let's take a gander at THIS animation ════════════════════ Now let's take our FIRST gentle forray into circuits. An electrical circuit is called a circuit.... why????
An electrical circuit is ALWAYS composed of a power supply and wires. We aren't ever really concerned about a wire connected to the plus and minus parts of a battery because that's boring (there's nothing much for the electrons to do afterall). However, it starts to get interesting when we add one or more components to our circuit. We can add components to an electrical circuit in two ways, . If we add only one component to the circuit, our math isn't all that interesting since we in parallelMUST add one end to the wire leading to the positive terminal and one end leading to the negative terminal in order for our circuit to be completed... adding two or more components, then we care... Let's confine our conversations to capacitors (since that is our topic O' the day). If we drop a capacitor in a circuit with a battery we run a wire from the positive terminal lof the battery to one plate, and from the other plate to the negative terminal. That charges up the capacitor and we're in business. However, as noted before, adding two or more capacitors gets much more interesting. We can run them When we calculate the capacitance of the entire circuit, we add the reciprical of the capacitance of the capacitors in series. Let's say cap #1 above had a capacitance of 7.5 μf.To find the capacitance of the circuit we'd reverse 'em and add 'em: 1/ = 1/7.5 μfDon't forget to 1/x 'em when you're done We can also add the caps together in paralell: Which is a whole lot nicer when we're doing a circuit analysis since we just add the capicitance of both caps to get the total capacitance of the circuit. So if 7.5 μf then the total capacitance of the circuit is simply:
7.5 μf = 12.5μf
COURSEWORK: Problems: 26.4, 26.5, 26.6 (should be done!) 26.9, 26.13, 26.16, 26.20 ANSWERS: |

STUDY GUIDE: |